双调和方程边界加权残值法及其应用

本文证明了可用复变函数的广义多项式逼近解析函数,并给出了用加权残值法解双调和方程的若干可供选择的试函数模式。文章还导出了广义调和函数系,并证明了它在平面边界上是一个完备系,可作为权函数系。将这种方法用于解各类边界板的弯曲问题和弹性平面问题,具有计算量较小、精度较高的特点。

METHOD OF WEIGHTED RESIDUALS ON THE BOUNDARY OF DOUBLE COMPATIBILITY EQUATION & APPLICATION

This paper proves a method which uses generalized polynomials of function of complex variable to approach the analytic function, and supplies some patterns of trying function to choose. Moreover, the paper derives a generalized compatibility function system which is proved a complete system on the boundary of plate, and can be considered as the system of weight function. The method shows a quite high computational efficiency and a good accuracy when applied to solving the bending problems of plate with boundary of all kinds and the elastic plate problems.